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On verification tools implemented in the System for Automated Deduction
, 2003
"... Among the tasks of the Evidence Algorithm programme, the verification of formalized mathematical texts is of great significance. Our investigations in this domain were brought to practice in the last version of the System for Automated Deduction (SAD). The system exploits a formal language to repre ..."
Abstract

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Among the tasks of the Evidence Algorithm programme, the verification of formalized mathematical texts is of great significance. Our investigations in this domain were brought to practice in the last version of the System for Automated Deduction (SAD). The system exploits a formal language to represent mathematical knowledge in a "natural" form and a sequential firstorder formalism to prove statements in the frame of a selfcontained mathematical text. In the paper, we give an overview of the architecture of SAD and its verification tools. In order to demonstrate the work of SAD, a sample verification session is examined.
Evidential Paradigm and Intelligent Mathematical Text Processing
"... Abstract: This paper presents the evidential paradigm of computersupported mathematical assistance in “doing ” mathematics and in reasoning activity. At present, the evidential paradigm is implemented in the form of System for Automated Deduction (SAD). The system is based on the methods of automat ..."
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Abstract: This paper presents the evidential paradigm of computersupported mathematical assistance in “doing ” mathematics and in reasoning activity. At present, the evidential paradigm is implemented in the form of System for Automated Deduction (SAD). The system is based on the methods of automated theorem proving and is intended for intelligent mathematical text processing. It proves mathematical theorems, verifies validity of selfcontained mathematical texts and can be used for inference search in firstorder sequentbased logic as well. For humanlike representation of mathematical knowledge, SAD exploits an original formal language close to natural languages of scientific publications. Since the problem of automated text verification is of great importance for industrial applications (checking specifications, proving safety properties of network protocols, etc), the paper illustrates some principles and peculiarities of the evidential paradigm by means of exemplifying the verification of a part of a nontrivial mathematical text. 1